Use the connection you found to find the coordinates of B given that M (-7, 1) is the midpoint of A (3, -4) and B (x, y).

$$\text{Apply } M = \frac{(A_x + B_x)}{2}, \frac{(A_y + B_y)}{2}.$$

$$(-7, 1) = \frac{(3+x)}{2}, \frac{(-4+y)}{2}$$

Equate the two coordinates separately,

$$\frac{(3+x)}{2} = -7$$

$$\begin{aligned} \Rightarrow \quad 3 + x &= -14 \\ \Rightarrow \quad x &= -17 \end{aligned}$$

$$\frac{(-4+y)}{2} = 1$$

$$\begin{aligned} \Rightarrow \quad -4 + y &= 2 \\ \Rightarrow \quad y &= 6 \end{aligned}$$

Check: midpoint of $A(3, -4)$ and $B(-17, 6)$

$$= \frac{(3-17)}{2}, \frac{(-4+6)}{2} = (-7, 1).$$